On the semiclassical Einstein-Langevin equation

TL;DR

This paper introduces a semiclassical Einstein-Langevin equation incorporating quantum stress-energy fluctuations as stochastic sources, and solves it around Minkowski spacetime to explore gravitational fluctuations beyond standard perturbative quantum gravity.

Contribution

It presents a new dynamical equation for semiclassical gravity that includes quantum fluctuations as stochastic sources and provides explicit solutions demonstrating non-perturbative gravitational behavior.

Findings

Derived the Einstein-Langevin equation for semiclassical gravity.

Solved the equation around Minkowski spacetime with a conformal scalar field.

Showed potential for non-perturbative gravitational fluctuations.

Abstract

We introduce a semiclassical Einstein-Langevin equation as a consistent dynamical equation for a first order perturbative correction to semiclassical gravity. This equation includes the lowest order quantum stress-energy fluctuations of matter fields as a source of classical stochastic fluctuations of the gravitational field. The Einstein-Langevin equation is explicitly solved around one of the simplest solutions of semiclassical gravity: Minkowski spacetime with a conformal scalar field in its vacuum state. We compute the two-point correlation function of the linearized Einstein tensor. This calculation illustrates the possibility of obtaining some ``non-perturbative'' behavior for the induced gravitational fluctuations that cannot be obtained in perturbative quantum gravity.